The guitar work on "Midnight at the Oasis" was the reason this song was so very, very popular when it first hit the radio hit list. The fellow playing that guitar so wonderfully is named Amos Garrett. Quite a feat, to be the one guitarist who spawned a hit on this album by Maria Muldaur, when some of the other players on the effort were Ry Cooder, David Lindley (from Jackson Browne fame), Andrew Gold, Mac Rebennack (aka Dr. John), Clarence White, and David Nichtern.
Amos Garrett is one of those fellows everyone knows in the music business, but nowhere else. He was the successor to Mike Bloomfield and Elvin Bishop in Paul Butterfield's band. He was a partner in the trio with Doug Sahm (Texas Tornadoes, SDQ) and Gene Taylor (Fabulous Thunderbirds, Blasters).
The Canadian blues player sure laid down a masterpiece when he did this work for Muldaur. I would be willing to bet he was paid union scale. If so, he would have been well advised to have gone for a piece of the action.